Question: Kevin is $3$ times as old as Daniel. $4$ years ago, Kevin was $5$ times as old as Daniel. How old is Kevin now?
Explanation: We can use the given information to write down two equations that describe the ages of Kevin and Daniel. Let Kevin's current age be $k$ and Daniel's current age be $d$. The information in the first sentence can be expressed in the following equation: ${k = 3d}$ Four years ago, Kevin was $k - 4$ years old, and Daniel was $d - 4$ years old. The information in the second sentence can be expressed in the following equation: ${k - 4 = 5(d - 4)}$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$, it might be easiest to solve our first equation for $d$ and substitute it into our second equation. Solving our first equation for $d$, we get: ${d = \dfrac{k}{3}}$. Substituting this into our second equation, we get: $ {k - 4 = 5 (}{\frac{k}{3}} {- 4)} $ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 4 = \dfrac{5}{3} k - 20$. Solving for $k$, we get: $\dfrac{2}{3} k = 16$. $k = \dfrac{3}{2} \cdot 16 = 24$.